Well first of all grab the Nexus Mod Manager and the New Vegas Script Extender to make most mods work and to make modding in general a lot easier.
I’d probably start with some of the popular mods, like using Project Nevada. Adds some tweaks (that can be disabled freely using the menu included in-game) and gives you a bigger stock of weapons to play with, plus letting you make the custom weapons from Fallout 3. Higher-tier helmets even come with custom night-vision and infrared vision.
Although really you should just take a browse around the New Vegas Nexus and she what you might like.
Oh yeah, if you hate that green/orange tint in either FO3 or New Vegas, grab Fellout so you can remove it. And maybe Electro-City if you want some more electric lights out in the wasteland. (do mind that this makes the nights quite a bit darker)
Well the great thing about the Laser Rifle is that with weapon mods it becomes the perfect sniper weapon. Plus you can craft souped up cells to power it up even more. Mad Bomber perk also lets you use spare MF Cells to make some disproportionately powerful grenades.
ED-E. Strong laser, nice little quest, and also functions as a portable workbench and reloading table when you install Lonesome Road. Little guy’s a lifesaver. As for human companions, it would be Arcade Gannon for me.
I usually play a bit of all, with special attention to Explosives perks, Shotgun perks, and some energy ones.
I don’t touch companions. Their AI is too moronic to be of any real help.
I prefer stealth gunner as well. Dropping one member of a spawn before the fight gets underway is huge. I try not to fixate on any one weapon - there’s just not enough ammo of any one type to get you through the game - but the “Guns” skill is broad enough to cover all the bases. Scoped gun for sniping, assault rifle for general purpose, shotgun for in close, pistol for small fries. Occasionally grenades if I can get the range right - they pack a wallop even without investing much in Explosives.